The circle method, invented by Hardy and Ramanujan and developped by Hardy and Littlewood and Kloosterman, is one of the most versatile methods currently available to determine the asymptotic behavior of the number of integral solutions to polynomial equations, when the number of solutions is sufficiently large.

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Content

The circle method, invented by Hardy and Ramanujan and developped by Hardy andLittlewood and Kloosterman, is one of the most versatile methods currently availableto determine the asymptotic behavior of the number of integral solutions topolynomial equations, when the number of solutions is sufficiently large.

The lecture will present an introduction to this method. In particular, it willpresent the solution of Waring's Problem concerning the representability of integersas sums of a bounded numbers of (fixed) powers of integers.